I did not read all of the receding replies as deeply as I usually do. So, I hope this is no repetitive. The refrigerant oil used in R-12 systems is not the same kind, or compatible with, the oil used in R0134 refrigerant systems. After you evacuate the R-12 you need to remove the old oil and use the correct R-134 compatible oil.
That said, for our 1969 Shelby GT4500, which also has factory A/C, I opted to keep the original A/C system in place. I was able to (and still can) find R-12 on ebay. It is a lot more than it was back in the 70s and 80s, but at least it is still available, although the writing on the outside is Japanese. All I know is it works. And the equipment used to pump a strong vacuum down on an A/C system, and the manifold gauge set, also still work nicely. Lucky for me I was able to get the Receiver/Dryer, Condenser, and TXV I needed for our Shelby, and after installing the new parts and pumping it down and later recharging the system, it is working beautifully.
We did install aftermarket A/C kits with R-134 in our 1973 Mustangs (both were non-AC cars originally). We selected kits from Classic Air. They also have a division that specializes in oem A/C equipment for cars. If yo run into a pinch, whether using R-12 or R-134, they have an excellent support group available via phone Highly recommended.
https://www.originalair.com/
https://www.originalair.com/